Aggregate Growth:
Mass-fractal aggregates are partly described by the mass-fractal dimension, df, that defines the relationship between size and mass,
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R =α N1/ df
where is the lacunarity constant, R is the aggregate overall size and N is the number of primary particles in an aggregate. The mass-fractal dimension ranges from 1 to 3 in 3-d space. The growth of aggregates was first modeled using computer simulations in the 1980-90's. Some discussion of the approaches and results form these simulations will be given below. The Smoluchowski equation can also be modified for mass-fractal aggregation and this is of the most flexibility since generalized results and conditions can be determined. Additionally, self-
preserving distributions have been determined for the Smoluchowski approach that enable a general treatment of mass fractal aggregation.
Simulation of Aggregation: